Nuclear electric propulsion (NEP) vehicles will be needed for future manned missions to Mars and beyond. Candidate designs must be identified for further detailed design from a large array of possibilities. Genetic algorithms have proven their utility in conceptual design studies by effectively searching a large design space to pinpoint unique optimal designs. This research combined analysis codes for NEP subsystems with a genetic algorithm. The use of penalty functions with scaling ratios was investigated to increase computational efficiency. Also, the selection of design variables for optimization was considered to reduce computation time without losing beneficial design search space. Finally, trend analysis of a reference mission to the asteroids yielded a group of candidate designs for further analysis.